Localization and delocalization for heavy tailed band matrices

Localization and delocalization for heavy tailed band matrices

We consider some random band matrices with band-width $N^\mu$ whose entries are independent random variables with distribution tail in $x^{-\alpha}$. We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when $\alpha

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Veröffentlicht in:Annales de l'I.H.P. Probabilités et statistiques 2014-11, Vol.50 (4), p.doi:10.1214/13-AIHP562
Hauptverfasser: Benaych-Georges, Florent, Péché, Sandrine
Format: Artikel
Sprache:eng
Schlagworte:
15A52
60F05
Band matrices
Heavy tailed random variables
Mathematics
Probability
Random matrices
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Zusammenfassung:We consider some random band matrices with band-width $N^\mu$ whose entries are independent random variables with distribution tail in $x^{-\alpha}$. We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when $\alpha
ISSN:0246-0203
1778-7017
DOI:10.1214/13-AIHP562